Limits to resolution in time-dependent spectral analysis of pulses

We present a study of the ability of three basic spectrometers—the diffraction grating, the Fabry–Perot, and the prism—to measure the Fourier energy spectra of pulses, that is, signals that are time limited. It is shown that under certain conditions prior knowledge of a finite upper bound on the maximum length of the input pulse can make it possible to violate the classical uncertainty principle and achieve enhanced spectral resolution. The resolution enhancement is obtained simply by recording the spectrometer output intensity only during a specific time interval after the entire pulse has been received.